Problem 1
The formula to use is
s = r*theta
where,
s = arc length
r = radius
theta = angle in radians
Note: if the angle is not in radians, you have to convert it over to radians. However, in this case we are told the angle is "5pi/4 radians". So no conversion is needed.
In this case,
s = unknown (this is what we want to solve for)
r = 34
theta = 5pi/4
keep in mind that 5pi/4 is the same as (5/4)*pi
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Plug the value of r and theta into the formula to get...
s = r*theta
s = 34*(5pi/4)
s = (34*5/4)*pi
s = 42.5*pi
s = 42.5*3.14
s = 133.45
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Final Answer: 133.45
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Problem 2
sin(angle) = opposite/hypotenuse
sin(61.7) = 8/y
y*sin(61.7) = 8
y = 8/sin(61.7)
y = 9.08598042654456 ... use a calculator
y = 9 ... rounding to the nearest whole number
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Final Answer: 9
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Problem 3
We need to know the length of BC. Let's call this x for now. Use the pythagorean theorem to find x
x^2 + 14^2 = 50^2
x^2 + 196 = 2500
x^2 + 196-196 = 2500-196
x^2 = 2304
sqrt(x^2) = sqrt(2304)
x = 48
So BC = 48 units long
Now we can compute the tangent of angle B
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tan(angle) = opposite/adjacent
tan(B) = AC/BC
tan(B) = 14/48
tan(B) = 7/24
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Final Answer: 7/24
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Problem 4
In this current stage, I cannot answer this question because the image isn't showing up. On my end, all I see is a black rectangle with no triangle showing. It seems like some kind of glitch is happening. Please repost this image. Thank you.
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Problem 5
There are multiple answers here so it seems like there should be a restriction. Does it state what the restriction must be? Please let me know. Thank you.
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Problem 6
Rule:
sin(x) = cos(90-x)
where x is an angle in degrees
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Using that rule mentioned above, we can replace the "sin(x)" term with "cos(90-x)" then solve for x
cos(63) = sin(x)
cos(63) = cos(90-x)
both arguments must be equal, so 63 must be equal to 90-x
63 = 90-x
63+x = 90-x+x
x+63 = 90
x+63-63 = 90-63
x = 27
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Final Answer: 27
Let's say each row has x desks and there are y rows.
We then know that x*y =25
We also know that x*2-5=y (number number of rows is five less than twice the number of desks in each row)
So we substitute: x*(x*2-5)=25
putting numbers out of the brackets:
2x*x-5x=25
2x*x-5x-25=0
(2x+5)(x-5)=0 (this bracketing is true: you can check it by expanding it:
2x*x-10x+5x-25
So that means that either x=-2.5which can't be : there can't be a fractional number of benches,
or x=5
so each row has 5 desks and there are 2*5-5 rows, or 5 rows.
Answer:
the largest is 620cm the next is 4.4 dam and the smallest is 0.52 km
Answer:
C) x = 12
Step-by-step explanation:
We can calculate the value of x using similarity ratio
x/8 = 9/6 cross multiply expressions
6x = 72 divide both sides by 6
x = 12
Let's first write the equation given
x²+6x-13=0
They have told us to use "Completing the square" method.
So we need write x²+6x-13 as a whole square.
x²+6x-13=0
x²+(2*3*x)-9-4 = 0
x²+(2*3*x)-3²=4
Now we can write the LHS as:
(x - 3)²=2²
Hence,
x-3 can either be 2 or -2
Now,
x - 3=2
x=5
Or,
x - 3=-2
x=1
Therefore now we know that x can either be 1 or 5. So the correct answer is Option B.
